Today in the morning I've found it doesn't work. The reason is that mysql is down.
I've restarted linux. The only visitor was me. But after short time mysql was down again (there were no visitors except me, so not big load). It repeated several times.

Later I've created 1GB swap file. For some time it was ok. So I thought that problem was solved. But later I found that mysql was down again. So 1,5 GB is not enough?

It seems like apache eats a lot of memory at some point. But I'm not sure.

Did anyone experience the same problem? Should I change any apache or mysql settings? I thought standard offer by DigitalOcean should work properly.

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I always build 512MB SWAP file and is enough to run Apache + MariaDB + WordPress. I run three WordPress blogs into same droplet (512 MB RAM).

I don't know what DO guys installed into the default WordPress image, but i suggest you to install byourself Apache + MariaDB + WordPress. You can find several tutorial and comentation into the DO community.

For this unexpected crashes i use one bash script that runs with cron every 10 min and check that some services are up (if they are down it restar them). Perhaps it helps you in the future, you can find it here